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Undergraduate Research & Mentoring Program Maseeh College of Engineering & Computer Science

2016

Design for Fractal Grid Generated Turbulence Design for Fractal Grid Generated Turbulence

Moira Gion Portland State University

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Citation Details Citation Details Gion, Moira, "Design for Fractal Grid Generated Turbulence" (2016). Undergraduate Research & Mentoring Program. 7. https://pdxscholar.library.pdx.edu/mcecs_mentoring/7

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Grid Design for Fractal Generated TurbulenceMoira Gion, Raúl Bayoán Cal

Objective• Design a set of passive grids with fractal geometry to be placed at the entrance

of a wind tunnel, acting as an inflow condition. • Quantities of interest are mean velocities, turbulence intensities, turbulence

decay, energy dissipation rate, anisotropy/isotropy, and the formation of vortices.

The observations obtained can contribute to the understanding of flow mixing by manipulating inflow conditions. Practical applications of this knowledge could include energy efficient mixing, heat dissipation techniques in electronics, forced convection.

Background & MotivationFluid flow is a dynamic system and it’s development is reliant on initial conditions. Turbulent flow often displays intermittency, or periodic phases, and self similar patterns. A fractal is a infinitely repeating self similar pattern. Kolmogorov’s theory used the idea of self-similarity to develop the statistical theory described by the energy cascade in turbulent flow.

In Kolmogorov’s energy cascade theory, the Reynold’s number based on Taylor microscale increases proportionally to the ratio of the integral length scale, L, to the Taylor microscale, λ. The Reynolds number,𝑅𝑒$ , is the ratio of inertial forces to viscous forces.

The Taylor microscale, 𝜆, is calculated by:

Previous studies for fractal generated turbulence using square grids have been performed by Hurst et. al (2007), Seoud et. al (2010), Gomes-Fernandes et. al (2012). In these studies they observed unusual behavior in turbulence, they found a constant ratio of integral scale to Taylor microscale as a function Reynolds number. In addition, turbulence intensities increased in the stream wise direction as the thickness ratio increased.

Design Process1) Geometry : Four fractal patterns were two-dimensionally sketched in

AutoCad. The open center grid was selected first for ease of design compared to the center space filled.

2) Properties: Values for length ratios, thickness ratio , and blockage ratio were chosen. The fractal dimension was determined based on the geometry of the design and describes the complexity of the shape.

3) Dimensions: Based off of the selected properties and the dimensions of the wind tunnel cross-section, the diameters of the circles were determined using an iterative process until all properties were met.

4) Fabricating & Material Considerations: Baltic birch plywood was chosen because of its stiffness and low comparable costs to other materials.

Results

Conclusion

Grid properties:• Fractal Dimension = 2• Length Ratio = 8• Thickness Ratio = 2.5• Blockage Ratio = 25% ± 0.5

Moving ForwardNext steps that need to be taken to meet the goal of the project are:

● Create a set of fractal grids with thickness ratios of 5 & 8, while keeping blockage ratio , length ratio , and fractal dimension constant.

● Create a center space filled grid , example reference fig . 2(a).● Collect data using Particle Image Velocimetry (PIV).

AcknowledgmentsThe authors acknowledge the support of the Semiconductor Research Corporation (SRC) Education Alliance (award # 2009-UR-2032G) and of the Maseeh College of Engineering and Computer Science (MCECS) through the Undergraduate Research and Mentoring Program (URMP).

Joe Ladd - PSU M.E.L.T. Team

Gomes-Fernandes, R., B. Ganapathisubramani, and J. C. Vassilicos. “Particle Image Velocimetry Study of Fractal-Generated Turbulence.”Journalof Fluid Mechanics711 (2012): 306–336. Web. 15 Oct. 2014.

Hurst, D., and J. C. Vassilicos. “Scalingsand Decay of Fractal-Generated Turbulence.”Physics of Fluids (1994-present)19.3 (2007): 035103. Web. 13 Jan. 2015

Mazellier, N., and J. C. Vassilicos. “Turbulence without Richardson–Kolmogorov Cascade.”Physics of Fluids22.7 (2010): 075101. Web. 16 Feb. 2015.Seoud, R. E., and J. C. Vassilicos. “Dissipation and Decay of Fractal-Generated Turbulence.”Physics of Fluids19.10 (2007): 105108. Web. 18 Feb. 2015.

This presentation poster was designed by FPPT.

Figure 3: Full scale grid tes ted in the wind tunnel for a fit check and vibrational observation.

• Circular geometry was chosen to design the grids to study the behavior of the induced flow from a fractal grid since previous studies have been done with square and I-beam patterns that contain mainy sharp edges.

• The fractal dimension of the circular fractal geometry was determined using the radius for the ratio of scale.

• The desired blockage ratio and thickness ratio were achieved by adjusting the inner diametters in a iterative design process.

• Material selected to build the bridge was baltic birch plwood and the grid was fabricated using a laser cutter.

• The grid succesfully showed little to no visual vibrations under desired incoming velocities.

• As the thickness ratio increases the thinnest bars will become thinner. It is recommended when doing so to look into stiffer materials in order to significant vibrations do not occur.

𝐷( =log(𝑁)log (𝑟)

𝑟= 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑠𝑐𝑎𝑙𝑒N=number o f copies𝐷(=Dimension

𝐿G = 𝑅H ∗ 𝐿J 𝑡K =𝑡LMN𝑡LOP

𝜎 =𝐴SKOT𝐴UVPPWX

𝐿 G = 𝑂𝑢𝑡𝑒𝑟 𝑟𝑎𝑑𝑖𝑢𝑠𝑎𝑡 𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑗𝑅H=Length Ratio𝐿 J= Initialouter radius

𝑡K = 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑟𝑎𝑡𝑖𝑜𝑡LMN =Thickness o f th ickestbar𝑡LOP =Thicknesso f th innestbar

𝑡K = 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑟𝑎𝑡𝑖𝑜𝑡LMN =Thickness o f th ickestbar𝑡LOP =Thicknesso f th innestbar

Figure 2: (a) Center space filled grid and (b) open center space grid

Figure 1: Self s imilar patterns can visually be seen when pouring coffee into your milk.

𝑅𝑒$ =𝑉𝜆𝜈

𝜆 =𝑢(𝑡)l

𝜕𝑢(𝑡)𝜕𝑡

l

𝑉 = 𝐼𝑛𝑐𝑜𝑚𝑖𝑛𝑔 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦𝜆=Taylor microsc al e𝜐=Kinematic viscosity

𝑢 = 𝐼𝑛𝑠𝑡𝑎𝑛𝑡𝑎𝑛𝑒𝑜𝑢𝑠 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦t= Time

a) b)